cat 2022 Question 10

Question

Suppose for all integers x, there are two functions f and g such that f(x) + f(x − 1) −1 = 0 and $g(x)=x^2$. If $f\left(x^2-x\right)=5$, then the value of the sum f(g(5)) + g(f(5)) is

Accepted Answer

Given,

f(x) + f(x−1) = 1 ...... (1)

f($x^2$−x) = 5 ...... (2)

g(x) = $x^2$

Substituting x = 1 in (1) and (2), we get

f(0) = 5

f(1) + f(0) = 1

f(1) = 1 - 5 = -4

f(2) + f(1) = 1

f(2) = 1 + 4 = 5

f(n) = 5 if n is even and f(n) = -4 if n is odd

f(g(5)) + g(f(5)) = f(25) + g(-4) = -4 + 16 = 12

Question 10.

Question Explanation